Wordpress Code Change Regarding Array Processing

I need some very specific code assistance from an experienced PHP developer. This is an urgent task, and requires strong knowledge of PHP arrays.

I have attached a document outlining the problem in detail, along with what I *think* needs to be changed. I just need someone to provide what I think is a single line of code, to get the desired results.

Please note that I will not be able to provide FTP access to the site in question, so I need someone who can simply message me the code to drop into place. I have provided detailed information in the attachment on where the change will need to be made.

Many thanks in advance!